Subtract:
[tex]\[
\begin{array}{r}
7x^2 - 5x + 3 \\
- \quad (2x^2 + 7x - 4) \\
\hline
\end{array}
\][/tex]

A. [tex]\(5x^2 + 12x - 1\)[/tex]
B. [tex]\(5x^2 - 12x + 7\)[/tex]
C. [tex]\(5x^2 - 2x + 7\)[/tex]
D. [tex]\(5x^2 + 2x - 1\)[/tex]



Answer :

To subtract the polynomials [tex]\((7x^2 - 5x + 3) - (2x^2 + 7x - 4)\)[/tex], we need to subtract the coefficients of like terms step by step.

### Step-by-Step Solution

1. Align the polynomials to make sure we subtract each corresponding coefficient:
[tex]\[ \begin{array}{r} 7x^2 - 5x + 3 \\ -\quad(2x^2 + 7x - 4) \\ \hline \end{array} \][/tex]

2. Distribute the negative sign across the second polynomial when subtracting each term:
[tex]\[ 7x^2 - 5x + 3 - (2x^2 + 7x - 4) = 7x^2 - 5x + 3 - 2x^2 - 7x + 4 \][/tex]

3. Combine like terms:
- [tex]\(x^2\)[/tex] terms: [tex]\(7x^2 - 2x^2 = 5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(-5x - 7x = -12x\)[/tex]
- Constant terms: [tex]\(3 + 4 = 7\)[/tex]

Putting it all together, we get:
[tex]\[ 5x^2 - 12x + 7 \][/tex]

### Conclusion

The resulting polynomial after subtraction is [tex]\(5x^2 - 12x + 7\)[/tex].

Therefore, the correct choice is:
B. [tex]\(5x^2 - 12x + 7\)[/tex]